For example, in multi-stage automatic transmissions that are mounted on vehicles and the like, linear solenoid valves can fail to be turned off in addition to frictional engagement elements (clutches and brakes) that are engaged in a normal operation. In this case, a friction engagement element that is supposed to be disengaged can be engaged. If all these friction engagement elements are simultaneously engaged, the automatic transmission can be stalled. Thus, valves for preventing such simultaneous engagement of the friction engagement elements (so-called cutoff valves) are typically provided. The cutoff valves prevent simultaneous engagement of the friction engagement elements by cutting off an engagement pressure of one friction engagement element when engagement pressures of these friction engagement elements are simultaneously applied.
However, as the number of stages of the automatic transmissions is increased for improved fuel consumption of vehicles or the like, a large number of friction engagement elements are required, and thus a large number of cutoff valves are required. This can hinder implementation of compact automatic transmissions, and reduction in cost.
Thus, it has been proposed to preset the engagement pressures of the friction engagement elements that are to be engaged in a normal operation to low pressures. Accordingly, the engagement pressures of the friction engagement elements that are to be engaged in a normal operation are calculated based on torque sharing of the friction engagement elements, so that the frictional engagement elements are engaged without slipping at each shift speed in the normal operation. If, e.g., any of linear solenoid valves fails to be turned off, and a friction engagement element that is supposed to be disengaged is engaged, the torque sharing changes, and one of the friction engagement elements slips due to the driving force of a drive source, and the driving force of driving wheels, whereby one of shift speeds is established (so that the stalled state is prevented). (see PCT International Patent Application Publication No. WO/2009/084294).
In PCT International Patent Application Publication No. WO/2009/084294, if, e.g., any of the linear solenoid valves actually fails to be turned off, and a friction engagement element that is supposed to be disengaged is engaged, one of the friction engagement elements slips. That is, a power-transmitting engagement element in that friction engagement element, and a power-receiving engagement element in that friction engagement element frictionally slip with respect to each other. If this state lasts for a long time, the frictionally slipping friction engagement element generates heat, which is not preferable in terms of durability.